Zonal Jet Creation from Secondary Instability of Drift Waves for Plasma Edge Turbulence

A new strategy is presented to explain the creation and persistence of zonal flows widely observed in plasma edge turbulence.The core physics in the edge regime of the magnetic-fusion tokamaks can be described qualitatively by the one-state modified Hasegawa-Mima(MHM for short)model,which creates enhanced zonal flows and more physically relevant features in comparison with the familiar Charney-Hasegawa-Mima(CHM for short)model for both plasma and geophysical flows.The generation mechanism of zonal jets is displayed from the secondary instability analysis via nonlinear interactions with a background base state.Strong exponential growth in the zonal modes is induced due to a non-zonal drift wave base state in the MHM model,while stabilizing damping effect is shown with a zonal flow base state.Together with the selective decay effect from the dissipation,the secondary instability offers a complete characterization of the convergence process to the purely zonal structure.Direct numerical simulations with and without dissipation are carried out to confirm the instability theory.It shows clearly the emergence of a dominant zonal flow from pure non-zonal drift waves with small perturbation in the initial configuration.In comparison,the CHM model does not create instability in the zonal modes and usually converges to homogeneous turbulence.

Numerical calculation of drift current in wind waves

-Drift current induced by wind and waves is investigated with phase-averaged Navier-Stokes equation in which the Reynolds stress is closed by k-ε model. The governing equations are solved by the finite volume method in a system of nonorthogonal coordinates which is fitted to the phase-averaged wave surface. The predicted drift current is fairly reasonable and the drag coefficient of sea-surface predicted with the newly developed interface conditions shows good agreement with previous measurements when breaking waves do not exist.

Formation of Nonlinear Solitary Vortical Structures by Coupled Electrostatic Drift and Ion-Acoustic Waves

Propagation of coupled electrostatic drift and ion-acoustic waves（DIAWs） is presented. It is shown that nonlinear solitary vortical structures can be formed by low-frequency coupled electrostatic DIAWs. Primary waves of distinct（small, intermediate and large） scales are considered. Appropriate set of 3 D equations consisting of the generalized Hasegawa-Mima equation for the electrostatic potential（involving both vector and scalar nonlinearities） and the equation of motion of ions parallel to magnetic field are obtained. According to experiments of laboratory plasma mainly focused to large scale DIAWs, the possibility of self-organization of DIAWs into the nonlinear solitary vortical structures is shown analytically. Peculiarities of scalar nonlinearities in the formation of solitary vortical structures are widely discussed.

The intermittent excitation of geodesic acoustic mode by resonant Instanton of electron drift wave envelope in L-mode discharge near tokamak edge

There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow.A long-lived standing wave phase,which we call the Caviton,and a short-lived traveling wave phase(in radial direction) we call the Instanton.Several abrupt phenomena observed in tokamaks,such as intermittent excitation of geodesic acoustic mode(GAM) shown in this paper,could be attributed to the sudden and fast radial motion of Instanton.The composite drift wave-zonal flow system evolves at the two well-separate scales:the micro-scale and the meso-scale.The eigenmode equation of the model defines the zero-order(micro-scale) variation;it is solved by making use of the two-dimensional(2 D) weakly asymmetric ballooning theory(WABT),a theory suitable for modes localized to rational surface like drift waves,and then refined by shifted inverse power method,an iterative finite difference method.The next order is the equation of electron drift wave(EDW) envelope(containing group velocity of EDW) which is modulated by the zonal flow generated by Reynolds stress of EDW.This equation is coupled to the zonal flow equation,and numerically solved in spatiotemporal representation;the results are displayed in self-explanatory graphs.One observes a strong correlation between the Caviton-Instanton transition and the zero-crossing of radial group velocity of EDW.The calculation brings out the defining characteristics of the Instanton:it begins as a linear traveling wave right after the transition.Then,it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz.The modulation to Reynolds stress in zonal flow equation brought in by the nonlinear Instanton will cause resonant excitation to GAM.The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.

The effect of forced oscillations on the kinetics of wave drift in an inhomogeneous plasma

The kinetics is analyzed of the drift of non-potential plasma waves in spatial positions and wavevectors due to plasma's spatial inhomogeneity. The analysis is based on highly informative kinetic scenarios of the drift of electromagnetic waves in a cold ionized plasma in the absence of a magnetic field(Erofeev 2015 Phys. Plasmas 22 092302) and the drift of long Langmuir waves in a cold magnetized plasma(Erofeev 2019 J. Plasma Phys. 85 905850104). It is shown that the traditional concept of the wave kinetic equation does not account for the effects of the forced plasma oscillations that are excited when the waves propagate in an inhomogeneous plasma.Terms are highlighted that account for these oscillations in the kinetic equations of the abovementioned highly informative wave drift scenarios.

Features of transport induced by ion-driven trapped-electron modes in tokamak plasmas

As an obstacle in high-performance discharge in future fusion devices,disruptions may do great damages to the reactors through causing strong electromagnetic forces,heat loads and so on.The drift waves in tokamak are illustrated to play essential roles in the confinement performance as well.Depending on the plasma parameters and mode perpendicular wavelength,the mode phase velocity is either in the direction of electron diamagnetic velocity(namely,typical trapped electron mode)or in the direction of ion diamagnetic velocity(namely,the ubiquitous mode).Among them,the ubiquitous mode is directly investigated using gyro-fluid simulation associating with gyro-fluid equations for drift waves in tokamak plasmas.The ubiquitous mode is charactered by the short wavelength and propagates in ion diamagnetic direction.It is suggested that the density gradient is essential for the occurrence of the ubiquitous mode.However,the ubiquitous mode is also influenced by the temperature gradients and other plasma parameters including the magnetic shear and the fraction of trapped electrons.Furthermore,the ubiquitous mode may play essential roles in the turbulent transport.Meanwhile,the relevant parameters are scanned using a great number of electrostatic gyro-fluid simulations.The stability map is taken into consideration with the micro-instabilities contributing to the turbulent transport.The stability valley of the growth rates occurs with the assumption of the normalized temperature gradient equaling to the normalized density gradient.

Basic features of the multiscale interaction between tearing modes and slab ion-temperature-gradient modes

Nonlinear interaction between tearing modes(TM) and slab ion-temperature-gradient(ITG) modes is numerically investigated by using a Landau fluid model. It is observed that the energy spectra with respect to wavenumbers become broader during the transition phase from the ITG-dominated stage to TM-dominated stage. Accompanied with the fast growth of the magnetic island, the frequency of TM/ITG with long/short wavelength fluctuations in the electron/ion diamagnetic direction decreases/increases respectively. The decrease of TM frequency is identified to result from the effect of the profile flattening in the vicinity of the magnetic island, while the increase of the frequencies of ITG fluctuations is due to the eigenmode transition of ITG induced by the large scale zonal flow and zonal current related to TM. Roles of zonal current induced by the ITG fluctuations in the instability of TM are also analyzed. Finally, the electromagnetic transport features in the vicinity of the magnetic island are discussed.

Role of the zonal flow in multi-scale multi-mode turbulence with small-scale shear flow in tokamak plasmas

The structural characteristics of zonal flows and their roles in the nonlinear interaction of multi-scale multi-mode turbulence are investigated numerically via a self-consistent Landau-fluid model.The multi-mode turbulence here is composed of a shorter wavelength electromagnetic(EM)ion temperature gradient(ITG)mode and a Kelvin-Helmholtz(KH)instability with long wavelengths excited by externally imposed small-scale shear flows.For strong shear flow,a prominent periodic intermittency of fluctuation intensity except for dominant ITG component is revealed in turbulence evolution,which onset time depends on the ion temperature gradient and the shear flow amplitudes corresponding to different KH instabilities.It is identified that the intermittency phenomenon results from the zonal flow dynamics,which is mainly generated by the KH mode and back-reacts on it.It is demonstrated that the odd symmetric components of zonal flow(same symmetry as the external flow)make the radial parity of the KH mode alteration through adjusting the drift velocities at two sides of the resonant surface so that the KH mode becomes bursty first.Afterwards,the ITG intermittency follows due to nonlinear mode coupling.Parametric dependences of the features of the intermittency are elaborated.Finally,associated turbulent heat transport is evaluated.

Texas Helimak

Helimak is an experimental approximation to the ideal cylindrical slab, a onedimensional magnetized plasma with magnetic curvature and shear. The Texas Helimak realizes this approximation to a large degree; the finite size of the device can be neglected for many phenomena. Specifically, the drift-wave turbulence characteristic of a slab is observed with scale lengths small compared with the device size. The device and the general features of its behavior are described here. The device is capable of studying drift-wave turbulence, scrape-off layer （SOL） turbulence, and the stabilization of turbulence by imposing velocity shear.

The theoretical study on intermittency and propagation of geodesic acoustic mode in L-mode discharge near tokamak edge

Through a systematically developed theory,we demonstrate that the motion of Instanton identified in Zhang et al(2017 Phys.Plasmas 24122304)is highly correlated to the intermittent excitation and propagation of geodesic acoustic mode(GAM)that is observed in tokamaks.While many numerical simulations have observed the phenomena,it is the first theory that reveals the physical mechanism behind GAM intermittent excitation and propagation.The preceding work is based on the micro-turbulence associated with toroidal ion temperature gradient mode,and slab-based phenomenological model of zonal flow.When full toroidal effect is introduced into the system,two branches of zonal flow emerge:the torus-modified low frequency zonal flow(TLFZF),and GAM,necessitating a unified exploration of GAM and TLFZF.Indeed,we observe that the transition from the Caviton to Instanton is triggered by a rapid zero-crossing of radial group velocity of drift wave and is found to be strongly correlated with the GAM onset.Many features peculiar to intermittent GAMs,observed in real machines,are thus identified in the numerical experiment.The results will be displayed in figures and in a movie;first for single central rational surface,and then with coupled multiple central rational surfaces.The periodic bursting first shown disappears as being replaced by irregular one,more similar to the intermittent characteristics observed in GAM experiments.

Observation of Low Frequency Instability in a Magnetized Plasma Column

Detailed analysis of the low frequency instability is performed in a linear magnetized steady state plasma device. Identification and modification of the instability are presented.

An experimental research on the instability of ion acoustic wave with electron drift

As electron temperature Te is much higher than ion temperature Ti, and electron driftspeed Vd is larger than the critical value Vdc of Vd, the ω=KVφ mode ion acoustic wave（IAW） will be instable. Under a long wave condition （KλD【【1, where λD is Deby length,K is weve number）, the growing rate γ（K） of the IAW may be written

Cyclokinetic models and simulations for high-frequency turbulence in fusion plasmas

Cyrokinetics is widely applied in plasma physics. However, this framework is limited to weak turbulence levels and low drift-wave frequencies because high-frequency gyro-motion is reduced by the gyro-phase averaging. In order to test where gyrokinetics breaks down, Waltz and Zhao developed a new theory, called cyclokinetics [R. E. Waltz and Zhao Deng, Phys. Plasmas 20, 012507 （2013）]. Cyclokinetics dynamically follows the high-frequency ion gyro-motion which is nonlineaxly coupled to the low-frequency drift-waves interrupting and suppressing gyro-averaging. Cyclokinetics is valid in the high-frequency （ion cyclotron frequency） regime or for high turbulence levels. The ratio of the cyclokinetic perturbed distribution function over equilibrium distribution function δf/F can approach 1. This work presents, for the first time, a numerical simulation of nonlinear cyclokinetic theory for ions, and describes the first attempt to completely solve the ion gyro-phase motion in a nonlinear turbulence system. Simulations are performed [Zhao Deng and R. E. Waltz, Phys. Plasmas 22（5）, 056101 （2015）] in a local flux-tube geometry with the parallel motion and variation suppressed by using a newly developed code named rCYCLO, which is executed in parallel by using an implicit time-advanced Eulerian （or continuum） scheme [Zhao Deng and R. E. Waltz, Comp. Phys. Comm. 195, 23 （2015）]. A novel numerical treatment of the magnetic moment velocity space derivative operator guarantee saccurate conservation of incremental entropy. By comparing the more fundamental cyclokinetic simulations with the corresponding gyrokinetic simulations, the gyrokinetics breakdown condition is quantitatively tested. Gyrokinetic transport and turbulence level recover those of cyclokinetics at high relative ion cyclotron frequencies and low turbulence levels, as required. Cyclokinetic transport and turbulence level are found to be lower than those of gyrokinetics at high turbulence levels and low-Ω＊ values with stable ion cyclotron modes. The gyrokinetic approximation is found to break down when the density perturbation exceeds 20%, or when the ratio of nonlinear E x B frequency over ion cyclotron frequency exceeds 20%. This result indicates that the density perturbation of the Tokamak L-mode near-edge is not sufficiently large for breaking the gyro-phase averaging. For cyclokinetic simulations with sufficiently unstable ion cyclotron （IC） modes and sufficiently low Ω^＊ ～10, the high-frequency component of the cyclokinetic transport can exceed that of the gyrokinetic transport. However, the low-frequency component of the cyclokinetic transport does not exceed that of the gyrokinetic transport. For higher and more physically relevant Ω^＊ ≥50 values and physically realistic IC driving rates, the low-frequency component of the cyclokinetic transport remains smaller than that of the gyrokinetic transport. In conclusion, the ＂L-mode near-edge short-fall＂ phenomenon, observed in some low-frequency gyrokinetic turbulence transport simulations, does not arise owing to the nonlinear coupling of high-frequency ion cyclotron motion to low-frequency drift motion.

A sensitivity analysis of millimeter wave characteristics of SiC IMPATT diodes

Ionization rate coefficients and saturation drift velocities for electrons and holes are the vital material parameters in determining the performance of an IMPATT diode.We have performed a sensitivity analysis of the millimeter wave characteristics of 4H-SiC and 6H-SiC IMPATT diodes with reference to the above mentioned material data and an operating frequency of 220 GHz.The effect of a small variation in the ionization rate and drift velocity on the device characteristics like break down voltage,efficiency,noise measure and power output has been presented here.